The set \(\mathcal {A}_{n,m}(\Psi )\)  is the limsup set of a sequence of
measurable subsets of \(I^{nm}\) . As such, its measure is 0 whenever
the measures of those subsets have a converging sum — a simple
consequence of the First Borel–Cantelli lemma (see, for example,
[1]}). Indeed, this is why, as we have mentioned,
the convergence parts of the theorems in the previous subsection are
straightforward to establish.
